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Quantum anonymous voting with unweighted continuous-variable graph states

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Abstract

Motivated by the revealing topological structures of continuous-variable graph state (CVGS), we investigate the design of quantum voting scheme, which has serious advantages over the conventional ones in terms of efficiency and graphicness. Three phases are included, i.e., the preparing phase, the voting phase and the counting phase, together with three parties, i.e., the voters, the tallyman and the ballot agency. Two major voting operations are performed on the yielded CVGS in the voting process, namely the local rotation transformation and the displacement operation. The voting information is carried by the CVGS established before hand, whose persistent entanglement is deployed to keep the privacy of votes and the anonymity of legal voters. For practical applications, two CVGS-based quantum ballots, i.e., comparative ballot and anonymous survey, are specially designed, followed by the extended ballot schemes for the binary-valued and multi-valued ballots under some constraints for the voting design. Security is ensured by entanglement of the CVGS, the voting operations and the laws of quantum mechanics. The proposed schemes can be implemented using the standard off-the-shelf components when compared to discrete-variable quantum voting schemes attributing to the characteristics of the CV-based quantum cryptography.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  2. Lucamarini, M., Mancini, S.: Secure deterministic communication without entanglement. Phys. Rev. Lett. 94(14), 140501 (2005)

    Article  ADS  Google Scholar 

  3. Hillery, M., Ziman, M., Bužek, V., Bieliková, M.: Towards quantum-based privacy and voting. Phys. Lett. A. 349(1), 75–81 (2006)

    Article  ADS  MATH  Google Scholar 

  4. Dolev, S., Pitowsky, I., Tamir, B.: A quantum secret ballot. preprint arXiv:quant-ph/0602087 (2006)

  5. Vaccaro, J.A., Spring, J., Chefles, A.: Quantum protocols for anonymous voting and surveying. Phys. Rev. A. 75(1), 012333 (2007)

    Article  ADS  Google Scholar 

  6. Horoshko, D., Kilin, S.: Quantum anonymous voting with anonymity check. Phys. Lett. A. 375(8), 1172–1175 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Li, Y., Zeng, G.: Quantum anonymous voting systems based on entangled state. Opt. Rev. 15(5), 219–223 (2008)

    Article  Google Scholar 

  8. Jiang, L., He, G., Nie, D., Xiong, J., Zeng, G.: Quantum anonymous voting for continuous variables. Phys. Rev. A 85(4), 042309 (2012)

    Article  ADS  Google Scholar 

  9. Hein, M., Eisert, J., Briegel, H.J.: Multiparty entanglement in graph states. Phys. Rev. A. 69(6), 062311 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Yu, S., Chen, Q., Lai, C.H., Oh, C.H.: Nonadditive quantum error-correcting code. Phys. Rev. Lett. 101(9), 090501 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Dr, W., Aschauer, H., Briegel, H.J.: Multiparticle entanglement purification for graph states. Phys. Rev. Lett. 91(10), 107903 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  12. Ghne, O., Tth, G., Hyllus, P., Briegel, H.J.: Bell inequalities for graph states. Phys. Rev. Lett. 95(12), 120405 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  13. Qian, Y., Shen, Z., He, G., Zeng, G.: Quantum-cryptography network via continuous-variable graph states. Phys. Rev. A. 86(5), 052333 (2012)

    Article  ADS  Google Scholar 

  14. Guo, Y., Lv, G., Zeng, G.: Balancing continuous-variable quantum key distribution with source-tunable linear optics cloning machine. Quant. Infor. Proces. 14(11), 4323–4338 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513–577 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Braunstein, S.L., Pati, A.K.: Quantum Information with Continuous Variables. Springer Science and Business Media, Berlin (2012)

    MATH  Google Scholar 

  17. Zhang, J., Braunstein, S.L.: Continuous-variable Gaussian analog of cluster states. Phys. Rev. A. 73(3), 032318 (2006)

    Article  ADS  Google Scholar 

  18. van Loock, P., Weedbrook, C., Gu, M.: Building Gaussian cluster states by linear optics. Phys. Rev. A. 76(3), 032321 (2007)

    Article  ADS  Google Scholar 

  19. Menicucci, N.C., Flammia, S.T., Zaidi, H., Pfister, O.: Ultracompact generation of continuous-variable cluster states. Phys. Rev. A. 76(1), 010302 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  20. Su, X., Tan, A., Jia, X., Zhang, J., Xie, C., Peng, K.: Experimental preparation of quadripartite cluster and Greenberger–Horne–Zeilinger entangled states for continuous variables. Phys. Rev. Lett. 98(7), 070502 (2007)

    Article  ADS  Google Scholar 

  21. Yukawa, M., Ukai, R., van Loock, P., Furusawa, A.: Experimental generation of four-mode continuous-variable cluster states. Phys. Rev. A. 78(1), 012301 (2008)

    Article  ADS  MATH  Google Scholar 

  22. Wu, Y., Cai, R., He, G., Zhang, J.: Quantum secret sharing with continuous variable graph state. Quantum Inf. Process. 13(5), 1085–1102 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Lau, H.K., Weedbrook, C.: Quantum secret sharing with continuous-variable cluster states. Phys. Rev. A. 88(4), 042313 (2013)

    Article  ADS  Google Scholar 

  24. Wang, G.Y., Li, T., Deng, F.G.: High-efficiency atomic entanglement concentration for quantum communication network assisted by cavity QED. Quantum Inf. Process. 14(4), 1305–1320 (2015)

    Article  ADS  MATH  Google Scholar 

  25. Wang, M., Xiang, Y., He, Q., Gong, Q.: Detection of quantum steering in multipartite continuous-variable Greenberger–Horne–Zeilinger Clike states. Phys. Rev. A. 91(1), 012112 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  26. Menicucci, N.C., Demarie, T.F., Brennen, G.K.: Anonymous broadcasting with a continuous-variable topological quantum code. arXiv preprint arXiv:1503.00717 (2015)

  27. Hein, M., Dr, W., Eisert, J., Raussendorf, R., Van den Nest, M., Briegel, H.-J.: Entanglement in graph states and its applications. arXiv preprint arXiv:quant-ph/0602096 (2006)

  28. Guo, Y., Qiu, D., Huang, P., Zeng, G.: Controlling continuous-variable quantum key distribution with tuned linear optics cloning machines. J. Phys. Soc. Jpn. 84, 094003 (2015)

    Article  ADS  Google Scholar 

  29. Wang, M., Sun, Y.: A practical, precise method for frequency tracking and phasor estimation. IEEE Trans. Power Del. 19(4), 1547–1552 (2004)

    Article  Google Scholar 

  30. Wang, M., Sun, Y.: A practical method to improve phasor and power measurement accuracy of DFT algorithm. IEEE Trans. Power Del. 21(3), 1054–1062 (2006)

    Article  Google Scholar 

  31. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86(5), 910 (2001)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61379153, 61572529), and partly by China Postdoctoral Science Foundation (Grant Nos. 2013M542119, 2014T70772), Science and Technology Planning Project of Hunan Province, China (Grant No. 2015RS4032).

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Authors and Affiliations

  1. School of Physics and Information Science, Hunan Normal University, Changsha, 410075, China

    Ying Guo & Yanyan Feng

  2. Information Science and Engineering, Central South University, Changsha, 410083, China

    Ying Guo

  3. Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Guihua Zeng

Authors
  1. Ying Guo
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  2. Yanyan Feng
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  3. Guihua Zeng
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Correspondence to Ying Guo.

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Guo, Y., Feng, Y. & Zeng, G. Quantum anonymous voting with unweighted continuous-variable graph states. Quantum Inf Process 15, 3327–3345 (2016). https://doi.org/10.1007/s11128-016-1349-1

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  • DOI: https://doi.org/10.1007/s11128-016-1349-1

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